Applications of tensor networks in graphical models and quantum circuit simulations

Tensor networks are powerful tools in quantum many-body problems，which are usually defined on lattices where efficient contraction algorithms exist. However, when applied to problems out of physics such as graphical models, the underlying network connections could be far from lattices.
In this talk I will introduce an approach for approximately contracting tensor networks with arbitrary connections, such as on lattices, random graphs, and complete graphs. We show applications of our algorithm in estimating free energy of finite-size spin glasses defined on various of topologies, where our algorithm outperforms existing algorithms including mean-field, MCMC based, and recently proposed neural network based methods. We further apply our algorithm to simulations of random quantum circuits with a low depth, where it displays significant speed up and memory efficiency over exact simulations while produces only negligible SVD cut-off error.